Answer
$x=64$
Work Step by Step
$x-4\sqrt{x}=32$
We make the substitution: $u=\sqrt{x}$. The equation then becomes:
$u^{2}-4u=32$
$ u^{2}-4u-32=0$
$(u-8)(u+4)=0$
$u-8=0$ or $u+4=0$
$u=8$ or $u=-4$
We convert the $u$ solutions to $x$ solutions:
$u=\sqrt{x}$
$x=u^2$
If $u=8$, then:
$x=8^2=64$
If $u=-4$, then that would mean $u=-4=\sqrt{x}$ which has no solution. So the only solution to the original equation is $x=64$
